| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Higher-frequency wave-field prediction | Helmholtz (test) | H1 Score0.422 | 32 | |
| Forward PDE solving | Helmholtz | Relative Error0.0072 | 26 | |
| PDE Solving | Helmholtz | RMSE (Helmholtz)0.222 | 17 | |
| Eigenvalue problem solving | Helmholtz Dimension: 6400 Precision: 1e-8 | Average Computation Time (s)31.31 | 17 | |
| Forward PDE Solving | Helmholtz 10K-epoch | Relative L2 Error1 | 16 | |
| Learning PDEs | Helmholtz 2D a=10 | Relative L2 Error0 | 15 | |
| Solving PDE | Helmholtz | Relative Error0.01 | 14 | |
| Physics-Informed PDE Solving | 2D Helmholtz (test) | Time (sec/iter)0.0228 | 14 | |
| Inverse PDE solving | Helmholtz full observations | Relative Error0.049 | 14 | |
| Forward PDE Solving | Helmholtz (test) | Relative H1 Error0.1385 | 12 | |
| Spatio-temporal PDE reconstruction | Helmholtz | PDE Residual0.55 | 12 | |
| PDE Reconstruction | Helmholtz synthetic (test) | RMSE0.022 | 10 | |
| PDE Reconstruction | Helmholtz 3% uniformly random measurements | Coefficient Relative L2 Error7.67 | 10 | |
| Inverse PDE solving | Helmholtz | Relative Error15.91 | 10 | |
| Neural Operator Learning | δ-Helmholtz | Relative L2 Error0.0013 | 9 | |
| Forward PDE solving | Helmholtz Full Observation | L2 Relative Error0.0108 | 9 | |
| Inverse problem | Helmholtz | PDE Residual0.2 | 9 | |
| Forward prediction | 2D Helmholtz | Relative L1 Error1.71 | 8 | |
| Shape Optimization and Inversion | Helmholtz | Inference Time (ms)0.47 | 8 | |
| PDE Inverse Problem | Helmholtz Noisy | L2 Relative Error67.93 | 7 | |
| PDE Forward Problem | Helmholtz Noisy | L2 Relative Error16.84 | 7 | |
| Inverse PDE Solving | Helmholtz | Relative L2 Error0.12 | 6 | |
| Forward PDE Solving | Helmholtz | Relative L2 Error0.025 | 6 | |
| Conditional source inference | Helmholtz 256 samples (test) | Relative L2 Error0.381 | 6 | |
| Operator Learning for PDEs | Helmholtz (downstream) | EG Score78.3 | 6 |